Legendrian mean curvature flow in $\eta$-Einstein Sasakian manifolds

Author:

Shu-Cheng Chang, Yingbo Han, Chin-Tung Wu

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-04-18 16:00:00

Abstract

Recently, there are a great deal of work done which connects the Legendrian isotopic problem with contact invariants. The isotopic problem of Legendre curve in a contact 3-manifold was studies via the Legendrian curve shortening flow which was introduced and studied by K. Smoczyk. On the other hand, in the SYZ Conjecture, one can model a special Lagrangian singularity locally as the special Lagrangian cones in C^{3}. This can be characterized by its link which is a minimal Legendrian surface in the 5-sphere. Then in these points of view, in this paper we will focus on the existence of the long-time solution and asymptotic convergence along the Legendrian mean curvature flow in higher dimensional {\eta}-Einstein Sasakian (2n+1)-manifolds under the suitable stability condition due to the Thomas-Yau conjecture.

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